Answer:
7x15+40=145
9.5x15=142.5
Step-by-step explanation:
To ensure Jackie barely wins the race with a 40m headstart against Marion, who runs at 9.5 m/s, we can calculate the distance of the race to be 112 meters, which Jackie will cover in 16 seconds at her speed of 7 m/s.
To determine how long the race should be so that Jackie barely wins over Marion Jones, we can utilize the concept of relative motion in physics. Given Marion's speed is 9.5 m/s and Jackie's speed is 7 m/s, and Jackie gets a 40m headstart, we can set up an equation to find the time it takes for Marion to catch up to Jackie.
We know the distance covered is speed times time, so for Marion: distance = 9.5 m/s time, and for Jackie: distance = 40m (headstart) + 7 m/s time. Since we are looking for the point where they are at the same distance we can set the equations equal to each other: 9.5 time = 40 + 7 time. Solving for time gives us:
9.5t = 40 + 7t
=> 2.5t = 40
=> t = 40 / 2.5
=> t = 16 seconds
Jackie will win the race if the race ends exactly when Marion catches up to her, so the race should be:
distance = 7m/s
16s = 112 meters
Therefore, the race needs to be 112 meters long for Jackie to barely win with a 40m headstart against Marion.
10. Alex is writing a number in scientific
notation. The number is greater than one
million and less than ten million. Which
number will Alex use as the exponent
of 10?
A 8
B 7
C 6
D 5
Answer:
C. 6
Step-by-step explanation:
Since the number is greater than one million and less than ten million, the number is seven digit which ranges from two million to nine million
Therefore, Alex will use 6 as the exponent
Linear system word problem
Answer:
1 year
Step-by-step explanation:
Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.
In this problem, "m" is the rate of growth in inches per year.
"b" is the starting height.
let "x" be the number of years
let "y" be the height in inches
Tree A: y = 8x + 3
Tree B: y = 9x + 2
Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.
8x + 3 = 9x + 2
8x + 3 - 3 = 9x + 2 - 3 Subtract 3 from both sides
8x = 9x - 1
8x - 9x = 9x - 9x - 1 Subract 9x form both sides
-x = -1 Divide both sides by -1 to isolate
x = 1 Number of years for the trees to be the same height
Therefore it will take 1 year for the trees to be the same height.
If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.
y = 8x + 3
y = 8(1) + 3
y = 11 Number of inches when trees are the same height
The cost of a company picnic varies directly as the number of employees attending the picnic. If a company picnic costs $487.50 for 30 employees, how much does a company picnic cost for 80 employees? ANSWER ASAP PLEASEEE
The company picnic cost $ 1300 for 80 employees
Solution:
Given that cost of a company picnic varies directly as the number of employees attending the picnic
Let "c" be the company picnic cost
Let "n" be the number of employees attending the picnic
Therefore,
[tex]cost \propto \text{ number of employees attending picnic }[/tex]
[tex]c \propto n\\\\c = kn[/tex]
Where "k" is the constant of proportionality
c = kn ---------- eqn 1
Given that company picnic costs $487.50 for 30 employees
Therefore substitute c = 487.50 and n = 30
[tex]487.50 = k(30)\\\\k = \frac{487.50}{30} = 16.25[/tex]
How much does a company picnic cost for 80 employees?
Substitute n = 80 and k = 16.25 in eqn 1
[tex]c = 16.25(80) = 1300[/tex]
Thus $ 1300 is the cost for 80 employees
Answer:
$1,300.00
Step-by-step explanation:
Molly has 9 cups of flour. If this is -
of the number she needs to make bread, how many cups does she need?
struct the tape diagram by reading it backward. Draw a tape diagram and label the unknown.
Answer:
9 pounds of flour
Step-by-step explanation:
mix together
A coin toss is based on what type of probability?
Answer:
50/50 chance
Step-by-step explanation:
Answer: Classical Probability (also know as priori or theoretical probability)
Step-by-step explanation:
I need help getting the answer to 1484 divided by 28
Answer:
53
Step-by-step explanation:
Find x in the given figure.
Answer:
Step-by-step explanation:
7x + 95+2x + x+25 + 90 = 360
10x + 210 = 360
10x = 360 -210
10x = 150
x = 150/10
x = 15
solve for x:3x=5x -8
Answer:
4
Step-by-step explanation:
3x = 5x - 8 is your equation. To solve for x, you want to get all the x's on the same side. You first subtract 5x from each side to get -2x = -8, and multiply both by 1- to get 2x = 8, and then divide both sides by 2 to find x = 4.
Answer:
Step-by-step explanation:
3x=5x -8
3x - 5x = - 8
-2x = -8
x = -8/-2
x = 4
4(x + 7) = 90(2+x)
4x + 28 = 180 + 90x
208 = 94x
What is the next step I have to do in solving this please help
Answer: 2.12
Step-by-step explanation: Divide by 94 on both sides to get X by itself
If Greg can build 1/7 of a brick wall in 1/12 of an hour whats his unit rate?
A: 1/84
B: 19/84
C: 1 5/7
D: 7
Final answer:
Greg's unit rate is [tex]1\frac{5}{7}[/tex] walls per hour, which is found by dividing 1/7 of a wall by 1/12 of an hour. The correct answer is option C: [tex]1\frac{5}{7}[/tex].
Explanation:
If Greg can build 1/7 of a brick wall in 1/12 of an hour, we want to find his unit rate, which is the amount of wall he can build per hour. To find Greg's unit rate, we divide the fraction of the wall built by the fraction of the hour spent building it. This calculation gives us:
Unit rate = (1/7) ÷ (1/12) = (1×12)/(7×1) = 12/7 = [tex]1\frac{5}{7}[/tex] walls per hour.
Therefore, the correct option is C: [tex]1\frac{5}{7}[/tex].
The function f(x) = −x2 + 44x − 384 models the hourly profit, in dollars, a shop makes for selling coffee, where x is the number of cups of coffee sold, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (4 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (4 points) Part C: Determine the y-intercept. What does this value mean in the context of the problem? (2 points) (10 points)
Answer:
Part A) The vertex is the point (22,100) see the explanation
Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation
Part C) The y-intercept is the point (0,-384) see the explanation
Step-by-step explanation:
Let
x ----> the number of cups of coffee sold
f(x) ---> the amount of profit
we have
[tex]f(x)=-x^{2} +44x-384[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
Part A) Determine the vertex. What does this calculation mean in the context of the problem?
Convert the quadratic equation in vertex form
Factor -1
[tex]f(x)=-(x^{2}-44x)-384[/tex]
Complete the square
[tex]f(x)=-(x^{2}-44x+22^2)-384+22^2[/tex]
[tex]f(x)=-(x^{2}-44x+484)+100[/tex]
Rewrite as perfect squares
[tex]f(x)=-(x-22)^{2}+100[/tex]
The vertex is the point (22,100)
That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22
Part B) Determine the x-intercepts. What do these values mean in the context of the problem?
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
so
we have
[tex]f(x)=-(x-22)^{2}+100[/tex]
For f(x)=0
[tex]0=-(x-22)^{2}+100[/tex]
solve for x
[tex](x-22)^{2}=100[/tex]
take square root both sides
[tex](x-22)=\pm10[/tex]
[tex]x=22\pm10[/tex]
so
[tex]x=22+10=32[/tex]
[tex]x=22-10=12[/tex]
The x-intercepts are the points (12,0) and (32,0)
That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero
Part C) Determine the y-intercept. What does this value mean in the context of the problem?
we know that
The y-intercept is the value of the function when the value of x is equal to zero
so
For x=0
[tex]f(x)=-x^{2} +44x-384[/tex]
substitute the value of x
[tex]f(x)=-(0)^{2} +44(0)-384[/tex]
[tex]f(x)=-384[/tex]
The y-intercept is the point (0,-384)
That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)
Find the midpoint of the line segment (-5,-8), (-7,3)
Answer:
Step-by-step explanation:
(-5,-8), (-7,3)
midpoint = (x₁+x₂/2, y₁+y₂/2)
= ( -5+-7/2 , -8+3/2) = (-5-7/2,-8+3/2)
= (-12/2, -5/2) = (-6,-5/2)
A circle with area 25pi has a sector with a central angle of 9/10pi radians. What is the area of a sector? Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal rounded to the nearest hundredth.
Answer:
11.25 pi
Step-by-step explanation:
Pi is 180 degrees, a circle is 360 degrees, 9/10's of 180 is 162, and divide that by the full 360 which is .45. Then, multiply that by 25 and you have 11.25 pi is the area of that sector.
if the measure of two exterior angles on the same side of the transversal are 3x and 7x+10, find the value of x
Answer:
The value of x is 17°.
Step-by-step explanation:
The two exterior angles on the same side of the transversal are always supplementary.
Therefore, if the measure of two exterior angles on the same side of the transversal are 3x and 7x+10, then we can write
3x + (7x + 10) = 180°
⇒ 10x = 180° - 10° = 170°
⇒ x = 17°
Therefore, the value of x is 17°. (Answer)
13x+2y=1
5x-2y=-19
Solve for x and y
Answer:
Step-by-step explanation:
13x+2y=1
+ 5x-2y=-19
-------------------
18x=18
x=1
5x1-2y=-19
5-2y=-19
-2y=-19-5
-2y=14
-y=7
y=-7
x=1
y=-7
To solve the system, eliminate variables, find [tex]\( x = -1 \)[/tex], then substitute into an equation to get [tex]\( y = 7 \)[/tex].
To solve the system of equations [tex]\(13x + 2y = 1\)[/tex] and [tex]\(5x - 2y = -19\)[/tex], you can use the method of elimination.
First, let's eliminate one of the variables. We can eliminate [tex]\(y\)[/tex] by adding the two equations together:
[tex]\[ (13x + 2y) + (5x - 2y) = 1 + (-19) \][/tex]
This simplifies to:
[tex]\[ 13x + 5x = -18 \][/tex]
[tex]\[ 18x = -18 \][/tex]
Now, divide both sides by 18:
[tex]\[ x = \frac{-18}{18} \][/tex]
[tex]\[ x = -1 \][/tex]
Now that we have found [tex]\(x\)[/tex], we can substitute it into one of the original equations to find [tex]\(y\)[/tex]. Let's use the first equation:
[tex]\[ 13(-1) + 2y = 1 \][/tex]
[tex]\[ -13 + 2y = 1 \][/tex]
Add 13 to both sides:
[tex]\[ 2y = 1 + 13 \][/tex]
[tex]\[ 2y = 14 \][/tex]
Divide both sides by 2:
[tex]\[ y = \frac{14}{2} \][/tex]
[tex]\[ y = 7 \][/tex]
So, the solution to the system of equations is [tex]\(x = -1\)[/tex] and [tex]\(y = 7\)[/tex].
5 - 3 = 15 or 7 +5 = 20 true or false
Answer:
False
Step-by-step explanation:
What is the sum or difference 2/3(7w+4) - 1/3(2w-1)
Answer:
4w+3
Step-by-step explanation:
2/3(7w+4)-1/3(2w-1)
14/3w+8/3-2/3w+1/3
14/3w-2/3w+8/3+1/3
12/3w+9/3
4w+3
What is
[tex] - |x + 2| + 1 = 4x - 6[/tex]
Answer:
x = 1
Step-by-step explanation:
Given
- | x + 2 | + 1 = 4x - 6 ( subtract 1 from both sides )
- | x + 2 | = 4x - 7 ( multiply both sides by - 1 )
| x + 2 | = - 4x + 7
The absolute value always returns a positive value, but the expression inside can be positive or negative, thus
x + 2 = - 4x + 7 ( add 4x to both sides )
5x + 2 = 7 ( subtract 2 from both sides )
5x = 5 ( divide both sides by 5 )
x = 1
OR
- (x + 2) = - 4x + 7, that is
- x - 2 = - 4x + 7 ( add 4x to both sides )
3x - 2 = 7 ( add 2 to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
As a check substitute these values into both sides of the equation and if both sides are equal then they are the solutions.
x = 1 : - |1 + 2| + 1 = - | 3 | + 1 = - 3 + 1 = - 2
right side = 4(1) - 6 = 4 - 6 = - 2 ← True
x = 3 : - |3 + 2| + 1 = - |5| + 1 = - 5 + 1 = - 4
right side = 4(3) - 6 = 12 - 6 = 6 ← False
Thus x = 3 is an extraneous solution and
x = 1 is the solution
Answer:
x = 1Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x+2|=\left\{\begin{array}{ccc}x+2&for&x+2\geq0\to x\geq-2\\-(x+2)&for&x<-2\end{array}\right[/tex]
[tex](1)\ x<-2\\\\-\bigg(-(x+2)\bigg)+1=4x-6\\\\+(x+2)+1=4x-6\qquad\text{combine like terms}\\\\x+(2+1)=4x-6\\\\x+3=4x-6\qquad\text{subtract 3 from both sides}\\\\x+3-3=4x-6-3\\\\x=4x-9\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\x-4x=4x-4x-9\\\\-3x=-9\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-9}{-3}\\\\x=3\notin(1)[/tex]
[tex](2)\ x\geq-2\\\\-(x+2)+1=4x-6\\\\-x-2+1=4x-6\\\\-x+(-2+1)=4x-6\\\\-x-1=4x-6\qquad\text{add 1 to both sides}\\\\-x-1+1=4x-6+1\\\\-x=4x-5\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x-4x=4x-4x-5\\\\-5x=-5\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-5}{-5}\\\\x=1\in(2)[/tex]
LeBron has 6 yards of cable.he needs 15 feet of cable to install a stereo.does he have enough cable to install the stereo?explain your answer
PLEASE MARK BRAINLIEST!
Answer:
Yes!Step-by-step explanation:
This is because 6 yards equals 18 feet. If there is 15 feet needed to install a stereo, and we have 18 feet of cable, we have MORE THAN ENOUGH cable to install the stereo. So yes, there is enough cable to install the stereo.
I hope this helps!
- sincerelynini
Answer:
Yes.
Step-by-step explanation:
There is 3 feet in every yard. So LeBron has 18ft of cable.
Round 639.13787717 to 2 decimal places.
Answer: 639.14
Step-by-step explanation:
A new energy drink advertises 106 calories for 8oz. How many calories are in 12oz of the drink?
12oz of the drink contains 159oz of calories.
To Calculate How many calories are in 12oz of the drinkA new energy drink advertises 106 calories for 8oz.
Based on the given conditions, formulate: 12*(106/8)
=12*(13.25)=159
Calories are in 12oz of the drink is 159oz
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The amount of money in an account can be determined by the formula A re where is the
initial investment, r is the annual interest rate, and tis the number of years the money was
invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest
compounded continuously?
Answer: $10272.17
Step-by-step explanation: Please see attachment for explanation
Answer:
[tex]\$10272.17[/tex]
Step-by-step explanation:
Since it is compounded continuously, we will use:
[tex]A=A_0 \cdot e^{k t}[/tex]
[tex]A_0[/tex] is the amount invested.
[tex]k[/tex] is the rate.
[tex]t[/tex] is the number of years you let the money sit.
[tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.
(Note:
I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)
[tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]
[tex]A=5000 \cdot e^{0.72}[/tex]
[tex]A=5000 \cdot 2.0544332[/tex] (approximated)
[tex]A=10272.16605[/tex] (approximated)
To the nearest cent this is [tex]\$10272.17[/tex].
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located? (0, 1) (1, 3) (1, 7) (2, 1)
Answer:
Step-by-step explanation:
If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k). If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.
[tex]f(1)=-2(1)^2+4(1)+1[/tex]
so f(1) = 3. Your choice is (1, 3)
The solution is (1, 3) where the vertex of the function located.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have
given that,
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1.
now, we have to find the vertex of the function.
If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).
If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.
now, putting the value of x as 1 ,
so, we get,
f(1) = –2(1)^2 + 4*1+ 1
=-2 + 4 +1
=3
so f(1) = 3.
The solution is (1, 3).
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evaluate y=3^x for x=2
Answer:
y=9
Step-by-step explanation:
substitution x=2 in equation
y= 3^2
y=9
Final answer:
To evaluate y=3^x for x=2, substitute x=2 into the expression y=3^x to find that y=9.
Explanation:
The given expression is y = 3^x. To evaluate y for x = 2, substitute x = 2 into the expression:
y = 3^2
y = 9
Therefore, y = 9 when x = 2.
Jacob has purchased a $129,000 home with a 30-year mortgage at 5.15%. He can make a monthly payment of $1000. If he were to make this
payment each month, how many months will it take him to pay off his mortgage? Round you answer to a whole number.
Answer: 188 months
Step-by-step explanation:
Principal = $129 000
Payment = $1000
Mortgage % = 5.15
Since,
Number of Months = log (1+[rate/(Payment/Principal)-rate] / log (1 + rate)
Also,
rate = 5.15/1,200 = 0.004292
Number of Months = log (1 + [0.004292/(1,000/129000) -0.004292] / log(1+0.004292)
Number of Months = log ( 1 + 0.004292/ ((0.007752 -0.004292) / log (1.004292)
Number of Months = log ( 1 + (0.004292/0.00346))/ log (1.004292)
Number of Months = log (1 + 1.240) / log (1.004292)
Number of Months = log (2.240) / log (1.004292)
Number of Months = 0.3502 / 0.001860
Number of Months = 188.28 months
Approximation to whole month,
Number of months = 188 Months.
What is the slope of a line that is parallel to the line containing (-11, 5) and (-6, 1)?
Answer:
(5-1)/-11-(-6) = -4/5
Step-by-step explanation:
since the lines are parallel they have same slope/gradient
Answer:
-4/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-5)/(-6-(-11))
m=-4/(-6+11)
m=-4/5
2. Choose all the expressions that are equal
to 2/3
1/6 + 1/2 yes or no
2/9 + 17/18 yes or no
5/12 + 1/4 yes or no
1 1/6-1/3 yes or no. 2 - 1 1/3 yes or no
Answer:
Yes, No, Yes, No, No
Step-by-step explanation:
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an airplane travels at a rate of 250 miles/he with the wind and at a rate of 150 miles against the wind. what is the rate of the wind?
50 miles per hour is the rate (speed) of the wind.
Step-by-step explanation:
Let consider the variable ‘x’ for speed of wind.
Below we write two values of the speed of the airplane in the air in terms of ‘x’:
1. Subtract wind speed from airplane speed: 250 - x.
2. Add wind speed to the airplane speed against the wind: 150 + x.
And now, set these above two expressions equal to each other to find x (wind speed),
250 – x = 150 + x
2x = 100
x = 50 miles per hour
if the sales tax rate is 7.25% in california, then how much would u pay in los angeles for a coat that cost $120.00
Answer:
The amount to be pay for coat is $128.70.
Step-by-step explanation:
Given:
The sales tax rate is 7.25% in California.
The cost for a coat in Los angeles is $120.00.
Now, to find amount to be paid.
Sales tax = 7.25%.
Cost = $120.00.
So, amount to be paid = $120 + 7.25% of $120.00.
[tex]=120+\frac{7.25}{100} \times 120.[/tex]
[tex]=120+\frac{870}{100}.[/tex]
[tex]=120+8.70[/tex]
[tex]=\$128.70[/tex]
Therefore, the amount to be pay for coat is $128.70.
Which pairs of triangles are similar? Check all that
apply.
AABC - ADEF
ADEF - AGHI
Ο ΔGHI - ΔABC
O AGHI - AJKL
AJKL - AABC
Answer:
JKL and ABC
DEF and GHI
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent
so
In this problem
1) triangles JKL and ABC are similar
because
[tex]\frac{KL}{BC} =\frac{JL}{AC}[/tex]
substitute the given values
[tex]\frac{10}{20} =\frac{7}{14}[/tex]
Simplify
[tex]\frac{1}{2} =\frac{1}{2}[/tex] ---> is true
therefore
The ratio of the corresponding sides is proportional
That means----> The triangles are similar
2) triangles DEF and GHI are similar
because
[tex]\frac{HI}{EF} =\frac{GI}{DF}[/tex]
substitute the given values
[tex]\frac{15}{10} =\frac{12}{8}[/tex]
Simplify
[tex]1.5=1.5[/tex] ---> is true
therefore
The ratio of the corresponding sides is proportional
That means----> The triangles are similar
The pairs of triangles that are similar to each other are:
B. ΔDEF ~ ΔGHI
E. ΔJKL ~ ΔABC
Similar TrianglesCorresponding angles of two triangles that are similar are always congruent, however, their corresponding sides are proportional to each other. This means, their ratio is equal.
Thus, triangles KJL and ABC are similar triangles because:
BC/KL = AC/JL = 2
Also, triangles DEF and GHI are similar triangles because:
GI/DF = HI/EF = 1.5
Therefore, the pairs of triangles that are similar to each other are:
B. ΔDEF ~ ΔGHI
E. ΔJKL ~ ΔABC
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